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Distribution of Brownian Local Time on Curves
Author(s) -
Davis Burgess
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609397003470
Subject(s) - mathematics , brownian motion , local time , graph , mathematics subject classification , brownian excursion , reflected brownian motion , distribution (mathematics) , constant (computer programming) , mathematical analysis , pure mathematics , combinatorics , geometric brownian motion , diffusion process , statistics , knowledge management , innovation diffusion , computer science , programming language
For all smooth nondecreasing functions f on [0, 1], the local time L f spent by standard Brownian motion on the graph of f satisfies P ( L f < x ) ⩾ P (2 L 0 < x ), for x > 0. The constant 2 in this inequality may not be replaced with a smaller one. 1991 Mathematics Subject Classification 60J55, 60J65.